A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to $N$-gluon final states in $q\bar{q}$ annihilation

TL;DR

This paper presents a novel application of the nested soft-collinear subtraction scheme to efficiently compute NNLO QCD corrections for gluonic jet production in hadron collisions, simplifying the handling of infrared singularities.

Contribution

It introduces a general method to identify and compute recurring structures in infrared subtraction terms, applicable to any partonic process at NNLO in QCD.

Findings

Successfully demonstrated cancellation of singularities in $q\bar{q} \to X + N g$ at NNLO

Derived simple formulas for the finite remainder of NNLO corrections

The approach can be extended to arbitrary processes at NNLO in QCD

Abstract

We describe how the nested soft-collinear subtraction scheme [1] can be used to compute the next-to-next-to-leading order (NNLO) QCD corrections to the production of an arbitrary number of gluonic jets in hadron collisions. We show that the infrared subtraction terms can be combined into recurring structures that in many cases are simple iterations of those terms known from next-to-leading order. The way that these recurring structures are identified and computed is fairly general, and can be applied to any partonic process. As an example, we explicitly demonstrate the cancellation of all singularities in the fully-differential cross section for the $q\bar{q} \to X + N g $ process at NNLO in QCD. The finite remainder of the NNLO QCD contribution, which arises upon cancellation of all $\epsilon$-poles, is expressed via relatively simple formulas, which can be implemented in a numerical code in a straightforward way. Our approach can be extended to describe arbitrary processes at NNLO in QCD; the largest remaining challenge at this point is the combinatorics of quark and gluon collinear limits.